Threshold Autoregressive (TAR) Model with exogenous variables (TARX)

Anyone have experience with these models? From what I remember about VAR is that adding exogenous variables to model a VARX is straightforward. Simply specify the VAR with the exogenous variables as independent variables and estimates are consistent.

So is a TAR model the same?

TAR models are estimated via nonlinear least squares, so presumably the inclusion of exogenous variables into the model should be no different than the case of a VAR model. Right?